Assertion : $\frac{5}{3}$ and $\frac{5}{4}$ are the eccentricities of two hyperbolas which are conjugate to each other. Reason: If $e$ and $e_{1}$ are the eccentricities of two conjugate hyperbolas then $e e_{1} > 1$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
We know if $e$ and $e_{1}$ are eccentricities of conjugate hyperbolas then
$\frac{1}{e^{2}} + \frac{1}{e_{1}^{2}} = 1$
Thus Assertion is correct.
Also eccentricity of any hyperbola is greater than one $∴ e e_{1} > 0$
Therefore, both statement are correct but Assertion is not explained by Reason.
Hence, option 'B' is correct.

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